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[libc][stdfix] Add exp function for short _Accum and _Accum types. (#…
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,92 @@ | ||
| //===-- Implementation of exphk function ----------------------------------===// | ||
| // | ||
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. | ||
| // See https://llvm.org/LICENSE.txt for license information. | ||
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #include "exphk.h" | ||
| #include "src/__support/CPP/bit.h" | ||
| #include "src/__support/common.h" | ||
| #include "src/__support/fixed_point/fx_bits.h" | ||
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| namespace LIBC_NAMESPACE { | ||
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| namespace { | ||
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| // Look up tables for exp(hi) and exp(mid). | ||
| // Generated with Sollya: | ||
| // > for i from 0 to 89 do { | ||
| // hi = floor(i/8) - 5; | ||
| // m = i/8 - floor(i/8) - 0.5; | ||
| // e_hi = nearestint(exp(hi) * 2^7) * 2^-7; | ||
| // e_mid = nearestint(exp(m) * 2^7) * 2^-7; | ||
| // print(hi, e_hi, m, e_mid); | ||
| // }; | ||
| // Notice that when i = 88 and 89, e_hi will overflow short accum range. | ||
| static constexpr short accum EXP_HI[12] = { | ||
| 0x1.0p-7hk, 0x1.0p-6hk, 0x1.8p-5hk, 0x1.1p-3hk, 0x1.78p-2hk, 0x1.0p0hk, | ||
| 0x1.5cp1hk, 0x1.d9p2hk, 0x1.416p4hk, 0x1.b4dp5hk, 0x1.28d4p7hk, SACCUM_MAX, | ||
| }; | ||
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| static constexpr short accum EXP_MID[8] = { | ||
| 0x1.38p-1hk, 0x1.6p-1hk, 0x1.9p-1hk, 0x1.c4p-1hk, | ||
| 0x1.0p0hk, 0x1.22p0hk, 0x1.48p0hk, 0x1.74p0hk, | ||
| }; | ||
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| } // anonymous namespace | ||
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| LLVM_LIBC_FUNCTION(short accum, exphk, (short accum x)) { | ||
| using FXRep = fixed_point::FXRep<short accum>; | ||
| using StorageType = typename FXRep::StorageType; | ||
| // Output overflow | ||
| if (LIBC_UNLIKELY(x >= 0x1.64p2hk)) | ||
| return FXRep::MAX(); | ||
| // Lower bound where exp(x) -> 0: | ||
| // floor(log(2^-8) * 2^7) * 2^-7 | ||
| if (LIBC_UNLIKELY(x <= -0x1.63p2hk)) | ||
| return FXRep::ZERO(); | ||
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| // Current range of x: | ||
| // -0x1.628p2 <= x <= 0x1.638p2 | ||
| // Range reduction: | ||
| // x = hi + mid + lo, | ||
| // where: | ||
| // hi is an integer | ||
| // mid * 2^3 is an integer | ||
| // |lo| <= 2^-4. | ||
| // Then exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo) | ||
| // ~ exp(hi) * exp(mid) * (1 + lo) | ||
| // with relative errors < |lo|^2 <= 2^-8. | ||
| // exp(hi) and exp(mid) are extracted from small lookup tables. | ||
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| // Round-to-nearest 1/8, tie-to-(+Int): | ||
| constexpr short accum ONE_SIXTEENTH = 0x1.0p-4hk; | ||
| // x_rounded = floor(x + 1/16). | ||
| short accum x_rounded = ((x + ONE_SIXTEENTH) >> (FXRep::FRACTION_LEN - 3)) | ||
| << (FXRep::FRACTION_LEN - 3); | ||
| short accum lo = x - x_rounded; | ||
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| // Range of x_rounded: | ||
| // x_rounded >= floor((-0x1.628p2 + 0x1.0p-4) * 2^3) * 2^-3 | ||
| // = -0x1.6p2 = -5.5 | ||
| // To get the indices, we shift the values so that it start with 0. | ||
| // Range of indices: 0 <= indices <= 89 | ||
| StorageType indices = cpp::bit_cast<StorageType>((x_rounded + 0x1.6p2hk) >> | ||
| (FXRep::FRACTION_LEN - 3)); | ||
| // So we have the following relation: | ||
| // indices = (hi + mid + 44/8) * 8 | ||
| // That implies: | ||
| // hi + mid = indices/8 - 5.5 | ||
| // So for lookup tables, we can use the upper 4 bits to get: | ||
| // exp( floor(indices / 8) - 5 ) | ||
| // and lower 3 bits for: | ||
| // exp( (indices - floor(indices)) - 0.5 ) | ||
| short accum exp_hi = EXP_HI[indices >> 3]; | ||
| short accum exp_mid = EXP_MID[indices & 0x7]; | ||
| // exp(x) ~ exp(hi) * exp(mid) * (1 + lo); | ||
| return (exp_hi * (exp_mid * (0x1.0p0hk + lo))); | ||
| } | ||
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| } // namespace LIBC_NAMESPACE |
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| //===-- Implementation header for exphk -------------------------*- C++ -*-===// | ||
| // | ||
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. | ||
| // See https://llvm.org/LICENSE.txt for license information. | ||
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception | ||
| // | ||
| //===----------------------------------------------------------------------===// | ||
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| #ifndef LLVM_LIBC_SRC_STDFIX_EXPHK_H | ||
| #define LLVM_LIBC_SRC_STDFIX_EXPHK_H | ||
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| #include "include/llvm-libc-macros/stdfix-macros.h" | ||
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| namespace LIBC_NAMESPACE { | ||
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| short accum exphk(short accum x); | ||
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| } // namespace LIBC_NAMESPACE | ||
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| #endif // LLVM_LIBC_SRC_STDFIX_EXPHK_H |
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